Probe head for scanning the surface of a workpiece

ABSTRACT

A measurement system has a surface sensing device mounted on an articulating probe head, which in turn is mounted on a coordinate positioning apparatus. The surface sensing device is moved relative to a surface by driving at least one of the coordinate positioning apparatus and probe head in at least one axis to scan the surface. The surface sensing device measures its distance from the surface and the probe head is driven to rotate the surface sensing device about at least one axis in order to control the relative position of the surface sensing device from the surface to within a predetermined range in real time.

This is a Division of U.S. patent application Ser. No. 11/919,066 filedOct. 23, 2007, which in turn is a National Phase of Patent ApplicationNo. PCT/GB2006/001298 filed Apr. 10, 2006. The disclosure of each ofthese prior applications is incorporated herein by reference in itsentirety.

The present invention relates to a method of scanning the surface of aworkpiece using a motorised scanning head mounted on a coordinatepositioning apparatus such as a coordinate measuring machine (CMM),machine tool, manual coordinate measuring arm and inspection robot.

It is known from International Patent Application No. WO90/07097 tomount a motorised scanning head on a coordinate positioning machine. Themotorised scanning head enables a stylus mounted on the motorisedscanning head to be rotated about two orthogonal axes. Thus the stylusmay be positioned angularly about these two axes whilst the motorisedscanning head can be positioned by the coordinate positioning machine inany position within the working volume of the machine.

Such a motorised scanning head provides a coordinate positioning machinewith greater scanning flexibility because the motorised scanning headcan position the stylus in many different orientations.

International patent application number WO 90/07097 further disclosesthat the rotary axes of the motorised scanning head may be operated ineither positioning mode or biasing mode. The biasing mode enablessurfaces to be scanned with a constant torque applied by the motors ofthe motorised scanning head. This patent application also discloses thata strain gauge array may be provided on the stylus to detect the forcesacting on the stylus. Data from the strain gauges is used to adjust thetorque applied by the motorised scanning head to keep the forces actingon the stylus as constant as possible.

In order to achieve high speed scanning with accuracy, it is desirableto minimise moving mass, and therefore dynamic errors, in the metrologysystem. A motorised scanning head allows high accelerations about itsrotary axes and is thus suitable for use in high speed scanning.

During the scan the tip of the stylus must be kept in contact with thesurface of the part being scanned. For known part scanning, the CMM andmotorised scanning head can follow a prescribed path. However, for anunknown part, the path of the stylus tip needs to be adjusted to keep iton the surface of the part but without exceeding a force which coulddamage the stylus of the probe or cause collision with the part.

Although the motors of the motorised scanning head may apply a constanttorque, factors such as acceleration, gravity and surface frictioninfluence the force felt at the stylus tip. Furthermore, the force feltat the stylus tip will vary with the angle of the stylus relative to thesurface. Thus constant torque does not necessarily result in constantstylus tip force. The method of using constant torque is thus notsuitable for high speed scanning because it does not ensure constantforce at the stylus tip.

High contact forces between the stylus tip and surface are required toensure the probe stays in contact with the surface. High speed scanningwith high forces is undesirable as it causes wear on the sensor. Thus itis desirable to minimise force. However, to measure low force with forcesensors such as strain gauges, the force sensors must be mounted on aflexible structure. Such a flexible structure is not robust and isliable to break if dropped or due to collision, therefore this is amajor obstacle to carrying out high speed scanning with constant force.Hence, there is a problem in sensing the small forces required for highspeed scanning with constant force at the probe tip.

High bandwidth force measuring probes which are required for high speedscanning generally have a short range. Therefore, any significantdeviations in the part from its expected form (for example due tomachining errors or fixturing etc) could result in the probe going outof range.

A first aspect of the present invention provides a measuring system inwhich a surface sensing device is mounted on a probe head, the probehead being mounted on a coordinate positioning apparatus;

-   -   wherein the coordinate positioning apparatus may be operated to        produce relative movement between the probe head and a surface        profile and wherein the probe head includes one or more drives        for producing rotational movement of the surface sensing device        about one or more axes;    -   wherein the surface sensing device is moved relative to the        surface by driving at least one of the coordinate positioning        apparatus and probe head in at least one axis to scan the        surface;    -   wherein the surface sensing device measures its distance from        the surface; and    -   wherein the probe head is driven to rotate the surface sensing        device about at least one axis in order to control the relative        position of the surface sensing device from the surface to        within a predetermined range in real time.

This has the advantage that the surface sensing device can be calibratedover a pre-defined range to maximise accuracy. Thus a better calibrationfit can be achieved by calibrating the surface sensing device over thispredetermined range than over the whole range of said device.

The surface sensing device may comprise a contact probe with adeflectable stylus, in this case the deflection is kept within apredetermined range.

The surface sensing device may comprise a non contact probe, such as acapacitance, inductance or optical probe. In this case, the offset iskept with a predetermined range.

The relative position of the surface sensing device from the surface maybe kept in the predetermined range by moving the surface sensing devicealong a deflection or offset vector. (The movement may either be in thesame or opposite direction as the vector.) For a two or threedimensional probe, the deflection or offset vector is established fromthe output of the surface sensing device. For a one dimensional probe,the deflection vector is equal to the surface normal which may beassumed from nominal data or predicted using historical data.

The movement of the surface sensing device relative to the surface bydriving at least one of the coordinate positioning apparatus and probehead in at least one axis can be produced by moving along a drive vectorwhich may be determined from the deflection or offset vector. The drivevector may be determined by rotating the deflection vector byapproximately 90°.

Feedback from the surface sensing device may be used to drive the probehead to adjust the distance of the surface sensing device in real time.

A second aspect of the present invention provides an articulating probehead on which a surface sensing device may be mounted, the articulatingprobe head providing rotational movement of the surface sensing deviceabout at least one axis;

-   -   wherein the probe head is provided with at least one rotary        measurement device to measure the angular position of the        surface sensing device about said at least one axis;    -   and wherein said at least one rotary measurement device is error        mapped.

Preferably the at least one rotary measurement device is error mappedseparately from other errors in the articulating probe head.

The at least one rotary measurement device may have a look up table,error function or Fourier series relating the measured angular positionof the surface sensing device to the error.

The at least one rotary measurement device may have a look up table,error function or Fourier series relating the measured angular positionof the surface sensing device to the corrected angular position of thesurface sensing device.

Examples of preferred embodiments of the invention will now be describedwith reference to the accompanying drawings wherein:

FIG. 1 is an elevation of a coordinate measuring machine includingscanning apparatus according to the present invention;

FIG. 2 is a cross-section of a motorised scanning head;

FIG. 3 illustrates a sweep scan of a plane surface;

FIG. 4 illustrates a scan of a bore;

FIG. 5 is a flow diagram illustrating the feedback system;

FIG. 6 illustrates a stylus tip on a surface with its associateddeflection and drive vectors; and

FIG. 7 illustrates historic data points used to predict a future surfacepoint;

FIG. 8 illustrates angular interferometry apparatus;

FIG. 9 is a side view of the scanning head coupled to a rotary table ina first orientation;

FIG. 10 is a side view of the scanning head coupled to a rotary table ina second orientation;

FIG. 11 illustrates non-contact apparatus for error mapping the encodersin the scanning head; and

FIG. 12 illustrates a second non-contact apparatus for error mapping theencoder in the scanning head.

FIG. 1 illustrates a motorised scanning head mounted on a coordinatemeasuring machine (CMM). A workpiece 10 to be measured is mounted on atable 12 of the CMM 14 and a motorised scanning head 16 is mounted on aquill 18 of the CMM 14. The spindle is driveable in the directions X, Y,Z relative to the table by motors in a known manner.

As illustrated in FIG. 2, the motorised scanning head 16 comprises afixed part formed by a base or housing 20 supporting a movable part inthe form of a shaft 22 rotatable by a motor M1 relative to the housing20 about an axis A1. The shaft 22 is secured to a further housing 24which in turn supports a shaft 26 rotatable by a motor M2 relative tothe housing 24 about an axis A2 perpendicular to the axis A1.

A probe 28 with a stylus 29 having a workpiece contacting tip 30 ismounted onto the motorised scanning head. The arrangement is such thatthe motors M1,M2 of the head can position the workpiece-contacting tipangularly about the axes A1 or A2 and the motors of the CMM can positionthe motorised scanning head linearly anywhere within thethree-dimensional coordinate framework of the CMM to bring the stylustip into a predetermined relationship with the surface being scanned.The motors M1,M2 are direct drive, which enables the motors to actquickly in response to demands from the controller.

Low friction bearings, such as air bearings (which have zero friction),also enable responsive high speed movement of the probe about the A1 andA2 axes. Air bearings have the further advantage that they are light.

Linear position transducers are provided on the CMM for measuring lineardisplacement of the scanning head and angular position transducers T1and T2 are provided in the scanning head for measuring angulardisplacement of the stylus about the respective axes A1 and A2. Thetransducers T1 and T2 are closely coupled to the load (i.e. the probe).This provides accurate position data of the probe. The bearings in thescanning head are stiff which ensures that the transducers T1 and T2 cangive accurate position data relative to earth.

The probe has a deflectable stylus 29 and transducers in the probemeasure the amount of stylus deflection. Alternatively a non contactprobe may be used. The probe may be one dimensional (e.g. a non-contactprobe which senses distance from surface), two dimensional (e.g. acontact probe sensing deflection in X and Y) or three dimensional (e.g.a contact probe sensing deflection in X, Y and Z).

On a vertical arm CNN as shown in FIG. 1, the A1 axis of the scanninghead 16 is nominally parallel to the CMM Z axis (which is along thespindle 18). The scanning head may rotate the probe continuously aboutthis axis. The A2 axis of the scanning head is orthogonal to its A1axis.

The motorised scanning head has a low inertia structure which makes itsuitable for high speed scanning. The low inertia structure is achievedby its small and light structure. The scanning head also has a stiffstructure and bearings which reduces measurement error.

A first embodiment of the invention is illustrated in FIG. 3 in which aplane surface 32 is scanned using a sweep scan profile 34.

The CMM moves the head along a path, whilst the motorised scanning headoscillates the probe about one rotary axis in a direction transverse tothe path of the CMM, creating a sinusoidal profile.

The deflection of the stylus 29 is measured by transducers in the probe.The deflection is kept as close as possible to a target value, within adesired range. The output from the probe 28 is sent to a controller. Ifthe deflection moves away from the target value, the angle of the probe28 about the other rotary axis of the motorised scanning head isadjusted to adjust the deflection and keep it close to the target value.

FIG. 4 illustrates a method of scanning a bore or circular profile withthe system. In this case, the motorised scanning head 16 is moved alongthe centre line 36 of the bore 38. The rotary axes A1,A2 of themotorised scanning head 16 are used to move the stylus tip 30 around theinner circumference of the bore, so that the combined motion of the CMMand motorised scanning head cause the stylus tip to move in a spiralpath about the inner surface of the bore.

At position A, one rotary axis is driving the probe and the other rotaryaxis is used to adjust the stylus deflection. At position B it is theother way around. In between the A and B positions, the two rotary axesact in combination to drive the probe along the spiral profile and toadjust deflection.

Other surface profiles may be measured using this technique, in whicheither one or both rotary axes is used to adjust deflection of the probeand the other or both of the rotary axes is used in driving the probe.

FIG. 5 is a flow diagram illustrating the feedback for control of stylusdeflection. The output P_(S) from the probe sensors 40 is sent to acentral processing unit (CPU) 42. The output may contain data in one,two or three dimensions.

The CPU 40 also receives positional inputs P_(X), P_(Y), P_(Z), P_(A1),P_(A2), from the encoders of the X,Y and Z axes of the CMM 44 and of theencoders of the A1 and A2 axes of the motorised scanning head 46. TheCPU 42 is able to calculate the surface position from the CMM dataP_(X), P_(Y), P_(Z), motorised scanning head data P_(A1), P_(A2) andprobe sensor data P_(S).

The CPU can also compare the measured stylus deflection to the targetvalue and the prescribed limits.

If the probe sensor is a 2D or 3D sensor, then the CPU can calculate thedeflection vector 50 of the stylus tip, which is illustrated in FIG. 6.This is the direction in which the stylus tip 30 is deflected. This isalso the direction parallel to which the position of the stylus tipshould be adjusted to keep the deflection within the prescribed limitsand as close to the target value as possible.

The deflection vector may also be used to generate the drive vector 52,which is the direction in which the stylus tip 30 is driven along thesurface 54. In order to generate the drive vector, the deflection vectoris rotated by approximately 900. The general direction is already known(e.g. from the CAD data, part programme, or from historical data points)but this calculation keeps the drive vector at a tangent to the surface.

Once the CPU has determined the drive vector and the deflection vector,it can send drive commands D_(X), D_(Y), D_(Z), D_(A1), D_(A2) to theCMM and motorised scanning head. Drive commands are sent to the X, Y, Zaxes and one or both of the motorised scanning head axes to drive thestylus tip along the drive vector. These commands are sent by voltage orcurrents to the respective motors.

Deflection adjustment commands are sent to one or both of the motorisedscanning head rotary axes in the form of a voltage or current to controlthe deflection in a direction parallel to the deflection vector.

Both deflection and drive are thus adjusted in real time using feedbackfrom the probe.

The CPU generates synchronised drive commands to the motorised scanninghead and the CMM. This ensures that the rotary motion provided by thescanning head does not get ahead of or lag behind the linear motion ofthe CMM. This synchronisation has the advantage that for scanningsurfaces, for example, free form surfaces, both the scanning head andCMM can provide motion about their respective axes in response to thedrive vector (e.g. to avoid unexpected obstacles).

In order for real time deflection control to be achieved, it isimportant that the probe sensors are able to produce fast and accuratemeasurements of the probe deflection. A fast and accurate method ofmeasuring probe deflection is by optical means.

European patent application EP 1,505,362 discloses optical transducersfor sensing deflection of a stylus holder into which a stylus ismounted. Each transducer includes a laser diode light source whichprojects a beam upon an optical feature, such as a mirror, located onthe stylus holder. Light reflected off the optical feature is incidentupon a position sensitive detector, the output of which is indicative ofthe incident position of the reflected light, and therefore of thedisplacement of the stylus holder.

U.S. Pat. No. 6,633,051 discloses a stylus assembly having a relativelystiff hollow stylus carrier and a relatively flexible hollow stylus. Anoptical transducer system is provided within the stylus assembly andcomprises a fixed light source which directs a beam of light towards astylus tip and a retro reflective component at the tip which reflectsthe beam back to a fixed detector. The arrangement is such that lateraldisplacement of the stylus tip when the tip is in contact with a surfacecan be measured directly. This arrangement has the advantage that theposition of the stylus tip is sensed, thus stylus bending is taken intoaccount.

Both of these arrangements have the advantage that they are light,responsive and have high resolution and the disclosures are incorporatedby reference into the present application.

In order for the probe to be suitable for high speed scanning, it needsto have high structural resonance, i.e. it must be sufficiently stiff inorder to follow the measurement path at a high speed. However, a stiffprobe has the disadvantage that it has a narrow range. Thus feedback isrequired to keep the probe within its measurement range.

This invention is also suitable with a non contact probe, such as acapacitance, inductance or optical probe. In this case, it is the offsetof the probe which is kept within prescribed limits, as close to anoffset target as possible. Outside the prescribed limits, the probe maynot behave linearly or may not be calibrated.

The non-contact probe may have a scalar sensor, in this case, the sensoroutput will give the distance from the surface but it will not give anyinformation about the direction. Thus on the sensor output alone, thereis not sufficient data to determine in which direction the probe needsto be moved in order to adjust the offset. Additionally, as thedeflection vector cannot be determined from the sensor data, the drivevector also cannot be determined.

In this case historical data can be used to determine an appropriatedeflection vector. As illustrated in FIG. 7, historical data points P1,P2 and P3 are used to predict the position of the next surface point P4on a surface 58. From this predicted position, the surface normal 56 atpoint P4 may also be predicted. This method is described in U.S. Pat.No. 5,334,918 which is incorporated herein by reference.

The deflection vector is taken to lie along the predicted surface normal56. Thus the position of the surface point is known from the measurementdata and the direction of the deflection vector is estimated usinghistorical data. The offset may be adjusted by moving one or both of therotary axes to move the probe along the deflection vector. The drivevector may be determined by rotating the deflection vector by 90° aspreviously described.

However, with two or three dimensional probes there is sufficient datafrom the sensors to determine the deflection vector without the use ofhistorical data.

The motorised scanning head is able to carry out a fast scan because ithas a high natural frequency and can thus position the probe tip at highspeed.

The motorised scanning head also has a high servo bandwidth. This meansthat it is able to move the probe over a large range of distances, thusit is effective in adjusting the deflection of the stylus. Furthermore,the movement of the motorised scanning head is controlled by directdrive motors which ensures a fast response to the commands from the CPU,thus enabling real time feedback to be possible.

The apparatus may be used with a range of different probes, for examplehaving different stylus lengths. The target deflection for each probemay be programmed into the controller. Therefore the probes may besubstituted for one another, with the motorised scanning head being ableto continue to use feedback to adjust the stylus deflection within thelimits of the particular probe. The probes may be calibrated so thatthey all have the same target deflection and range. Non contact probesmay be likewise calibrated so that the offset target and ranges are allthe same and correspond to the target deflection and range of contactprobes.

The motorised scanning head may be compensated for errors in its headgeometry in real time. Such errors may be created during assembly of themotorised scanning head. The scanning head is calibrated using knownmethods to understand its parameters. Such methods may comprisemeasuring a part of known dimensions, such as a datum ball, with thescanning head and thereby collecting the measurement errors which areused to calibrate the head. As the motorised scanning head iscalibrated, these errors are taken into account when driving the motorsof the head to adjust the position of the surface sensing device inresponse to the feedback.

The CMM is error mapped for rotary errors about its linear drive (e.g.pitch, roll and yaw). The scanning head is also error mapped for rotaryerrors. Measurement data is error corrected in real time for thecombined CMM and scanning head rotary errors, thus providingsynchronised error correction. It is also possible to use the same CMMand scanning head error mapping data to error correct the demand signalsto both the CMM and scanning head in real time for synchronised errorcorrection.

This method of high speed scanning is suitable for measuring unknownparts. The path the CMM is to follow may be programmed into thecontroller or controlled manually via a joystick. The scanning movementof the motorised scanning head, such as a sweep profile, is alsoprogrammed. During the scan, at least one rotary axis of the motorisedscanning head is driven to control deflection as previously described.The drive vector controlling the CMM and at least one axis of themotorised scanning head may also be adjusted as previously described.

The angular position transducers T1 and T2 in the motorised scanninghead may comprise rotary encoders. Off the shelf rotary encoders are notsufficiently accurate for the measurement requirements of the motorisedscanning head and so need to be error mapped.

The scanning head contains many sources of errors, for example geometricerrors and distortion caused by gravity or acceleration. It isadvantageous to create an error map for the encoders which is separatefrom other errors, such as geometric errors.

The rotary encoders may be error mapped either before or afterinstallation in the motorised scanning head. Error mapping the rotaryencoders after installation has the advantage that errors caused bymounting the encoders, such as distortions and eccentricities areaccommodated.

The encoders in the scanning head may be error mapped by driving thescanning head against a reference standard.

A first method of error mapping the encoders is described below withreference to FIG. 8, using an angular interferometer. A suitable angularinterferometer is disclosed in International Patent Application WO96/31752. The angular interferometer includes a laser 60 which generatesa beam of coherent light. A polarising beam splitter and prism 64 splitthe beam into a pair of orthogonally polarised, parallel extending beams66,68. The beams each pass through a glass block 70,72, respectively ofa refractive artefact mounted onto a mount 74 of the scanning head. Thebeams 66,68 are subsequently reflected back parallel to their incidentpath by a pair of retroreflectors 70,72, displaced one relative to theother in the direction of beam propagation by a distance equal to theseparation between the beams to reduce phase noise. The beams arerecombined to generate an interference beam. Rotation of the scanninghead results in change in relative path lengths of the beams 66 and 68and therefore a shift in the phase of the interference beam, which maybe used to determine angular displacement of the scanning head. Thebeams 66,68 are axially spaced, enabling the use of an artefact having arelative low moment of inertia and allowing a high range of angulardisplacement.

The refractive artefact is mounted on the motorised scanning head, whichis rotated about each axis individually whilst measurements are takenwith the scanning head encoders and the interferometer apparatus. Thetwo sets of measurement are used to create an error function or look uptable.

As the interferometer can only take reading over a finite angle, aslipping clutch arrangement is used so that the encoders can be errormapped over the whole range. The sets of measurement data from eachangular section are stitched together to create measurement data overthe whole range.

The error in the scanning head angle is taken from the differencebetween the recorded scanning head angle and the angular positionmeasured by the interferometer.

A second method of error mapping the encoders will now be described withreference to FIG. 9. FIG. 9 illustrates the motorised scanning head 16directly coupled to a calibrated rotary stage, with the direct couplingaligned with the A1 axis. The rotary stage has a fixed structure 82which is mounted onto a base and a rotatable structure 84 mounted onbearings to be rotatable relative to the fixed housing 82 about an axis.Rotary encoders are used to measure rotation of the rotatable structurerelative to the fixed structure. The coupling comprises a shaft 86 whichis mounted on the probe mount 88 of the scanning head 16. The shaft 86is torsionally stiff in rotation about its longitudinal axis but allowstranslation in X and Y and a small amount of tilt about all axes, apartfrom about its longitudinal axis.

The scanning head is then rotated about the A1 axis, whilst the encoderreadings in the scanning head are recorded simultaneously with theencoder readings in the rotary stage. The position reading from thescanning head encoders and calibrated rotary stage position readings maythen be compared.

The encoders of the A2 axis are error mapped, as illustrated in FIG. 10.The rotary table of FIG. 10 is mounted on its side, so that the shaft 86extends horizontally from the rotary table 80. An L-shaped plate 90 isprovided at the free end of the shaft and the horizontal portion of theL-shaped plate 90 is mounted onto the probe mount 88 of the probe head.The shaft 86 is thus aligned with the A2 axis. Therefore rotation of theprobe head 16 about its A2 axis causes rotation of the rotary part 84 ofthe rotary table 80. The scanning head is rotated about its A2 axiswhilst the encoder readings from both the scanning head and the rotarytable are recorded simultaneously.

The error in the scanning head reading is determined from the differencebetween the scanning head encoder reading and the rotary table encoderreading.

The encoders in the rotary table may be calibrated by the followingmethod. The scanning head 16 is coupled to the rotary table 80 asillustrated in FIG. 9 with the shaft 86 rigidly coupling the scanninghead and rotary table together.

After rotating the scanning head and coupled rotary table a predefinedamount (for example one rotation), the scanning head is rotated aboutits A1 axis relative to the rotary table and the process repeated atthis new alignment. By repeating the process at several rotationalalignments about the A1 axis, the measurement results may bemathematically manipulated so that the errors from only one encoder (inthis case the rotary encoder in the rotary table) are derived.

For the step of calibrating the encoders in the rotary table, thescanning head may be replaced by another device including a rotaryencoder, for example a second rotary table.

In an alternative method of calibrating the encoders in the rotarytable, a second rotary encoder is coupled directly to the rotary table.As before, the rotary table and second rotary encoder are rotatedtogether whilst recording the readings from both rotary encoders. Afterrotating a predefined amount (for example, one rotation) the secondrotary encoder is uncoupled and rotated about its axis to a new angularalignment. If incremental rather than absolute encoders are used, therotated rotary encoders must either continue to record their positionsas they are re-oriented, or must have reference markers so that theirtime positions can be established after re-orientation. The process isrepeated at several rotational alignments of the second rotary encoderabout its axis. As before, this enables the errors from only one encoderto be derived, thus enabling the rotary encoder in the rotary table tobe error mapped. This method has the advantage that as the second rotarytable is mounted on the same bearings as the encoder in the rotarytable, errors from the misalignment of bearings are eliminated.

FIG. 11 illustrates a variation on the method illustrated in FIG. 9. Inthis embodiment, the scanning head 16 is mounted directly above adetector 90, such as a CCD or psd. A light source 92 is mounted on themotorised scanning head 16 which produces a light beam 94 incident onthe detector 90. As the scanning head is rotated about its axis A1, theposition of the beam 94 incident on the detector 90 will change. Thusthe encoder reading can be compared with the position of the light beamon the detector.

The error in the scanning head angle is taken from the differencebetween the recorded scanning head angle and the recorded position ofthe light beam on the detector.

A look up table may be created to relate the reported scanning headangle and the error correction. Alternatively, a look up table may becreated to relate the reported scanning head angle and the correctedscanning head angle.

The error corrections for scanning head angles which lie betweenincrements in the look up table may be interpolated, for example bylinear or smooth interpolation.

A polynomial function may be defined to relate either the reportedscanning head angle to error or the reported scanning head angle tocorrect angle. This polynomial function may relate to the whole range ofangles. Alternatively, several polynomial functions may be defined, eachrelating to a ranges of angles.

Alternatively, the error function may be modelled as a Fourier series,with the coefficients of the Fourier series stored.

Another embodiment for mapping the encoders in the scanning head isillustrated in FIG. 12. In this apparatus, a collimated light source100, beam splitter 102 and optical detector 104, such as an x,y positionsensing detector (psd) are mounted onto the scanning head 16. Thescanning head 16 is positioned above a rotary stage which has arotatable plate 108 rotatably mounted by bearings on a fixed structure109. Rotary encoders are provided to measure the angular position of therotary plate 108. The rotary plate 108 is provided with an upright post110 on which is mounted a retroreflector 112.

When the optics on the scanning head 16 are aligned with theretroreflector 112, a light beam projected from the light source 100will pass through the beam splitter 102 to the retroreflector 112. Theretroreflector 112 reflects the beam back to the beam splitter whichreflects it onto the detector 104.

The rotatable plate 108 of the rotary stage is rotated at a constantspeed. The scanning head 16 is rotated about its A1 axis at a speedwhich matches the rotating plate, by keeping the beam incident on thedetector 104. Feedback from the detector 104 is used by the controllerto control the speed of the scanning head. Once the rotating plate 108and scanning head 16 are rotating at the same speed, the outputs of thetwo sets of encoders are simultaneously recorded, thus enabling thescanning head encoders to be error mapped.

As the scanning head 16 rotates, one of the channels of the x,y psdreports the difference in orientation between the rotary stage andreference encoder. The other channel of the psd reports any change inthe height of the retro-reflector with respect to the head and cantherefore report angular misalignments between the scanning head axisand the reference axis. These can be removed by adjusting the pitch androll of the rotary stage. The rotary stage is mounted on a pitch androll tilt stage 114, to enable this adjustment.

The only other possible misalignment is if the centre of rotation of thescanning head is not over the centre of rotation of the rotary stage.This can be seen as a sinusoidal difference between the scanning headand rotary stage encoder outputs which occurs once per revolution. Thex,y position of the head or stage can be altered to minimise this firstorder error. The axes of rotation of the scanning head and rotary stagewill then be coincident.

The remaining differences between the head encoder and the rotary stageencoder are then the ones of interest and can be used to error map theactive head encoders as previously described.

If the rotary stage encoder is not calibrated, multiple relative anglesbetween the scanning head and rotatable plate can be produced by movingthe retro-reflector post to a number of different angles on therotatable plate and repeating the data collection, in the same manner asdescribed when using the coupling shaft, enabling one encoder to beerror mapped.

The A2 axis of the scanning head can be mapped in the same way, with asimilar arrangement to that illustrated in FIG. 10 in which the rotarytable is mounted on its side and the optics are mounted on an L-shapedbracket.

The invention claimed is:
 1. An articulating probe head comprising; afirst member; a second member that is mounted for rotation with respectto the first member about a first axis: a third member that is mountedfor rotation with respect to the second member about a second axis, andon which a surface sensing device is mountable, the second and thirdmembers providing rotational movement of the surface sensing deviceabout the first and second axes; and a first rotary measurement deviceacting between the first and second members to measure an angularposition of the surface sensing device about the at least one firstaxis, wherein a first error map is provided that relates to, separatelyfrom other errors in the articulating probe head, measurements of theangular position made by the first rotary measurement device about thefirst axis,and wherein the first error map is derived from errors inmeasurement of the angular position of the third member about the firstaxis while the third member is mounted on the second member.
 2. Thearticulating probe head according to claim 1, wherein the error mapcomprises a look up table, error function or Fourier series relating themeasured angular position of the surface sensing device to themeasurement error.
 3. The articulating probe head according to claim 1,wherein the error map comprises a look up table, error function orFourier series relating the measured angular position of the surfacesensing device to the corrected angular position of the surface sensingdevice.
 4. A measuring system comprising: a motorized probe head, ontowhich a surface sensing device is mountable, the motorized probe headincluding: a first member: a second member that is mounted for rotationwith respect to the first member about a first axis; a third member thatis mounted for rotation with respect to the second member about a secondaxis, and on which the surface sensing device is mountable; a firstmotor acting between the first and second members to produce rotationalmovement of the surface sensing device about the first axis; and a firstrotary measurement device that measures the rotational movement aboutthe first axis; and the measuring system further comprising a processorthat is configured to receive a positional input from the first rotarymeasurement device and to send an output to control the first motor ofthe motorized probe head, wherein the first rotary measurement devicehas a calibration that is separate from other errors in the motorizedprobe head, wherein the calibration of the first rotary measurementdevice is derived from errors in measurement of the angular position ofthe third member about the first axis while the third member is mountedon the second member, and wherein the processor is configured tocompensate in real time for errors derived during the calibration of thefirst rotary measurement device when the processor creates the output tocontrol the first motor from the positional input.
 5. The measuringsystem according to claim 4, wherein the processor is further configuredto compensate for geometric errors of the motorized probe head.
 6. Themeasuring system according to claim 4, wherein the measuring systemincludes a coordinate positioning apparatus on which the motorized probehead is mounted.
 7. The measuring system according to claim 4, whereinthe first rotary measurement device is an encoder.
 8. The measuringsystem according to claim 4, wherein the motorized probe head furthercomprises: a second motor acting between the second and third members toproduce rotational movement of the surface sensing device about thesecond axis; and a second rotary measurement device that measures therotational movement about the second axis.
 9. The measuring systemaccording to claim 8, wherein the processor is configured to receive apositional input from the second rotary measurement device and to sendan output to control the second motor of the motorized probe head. 10.The measuring system according to claim 9, wherein the second rotarymeasurement device has a calibration that is separate from other errorsin the motorized probe head.
 11. The measuring system according to claim10, wherein the calibration of the second rotary measurement device isderived from errors in measurement of the angular position of the thirdmember about the second axis while the third member is mounted on thesecond member.
 12. The measuring system according to claim 9, whereinthe processor is configured to compensate in real time for errorsderived during the calibration of the second rotary measurement devicewhen the processor creates the output to control the second motor fromthe positional input from the second rotary measurement device.